Evaluate \( \frac{2\sin 30 + 5\tan 60}{\sin 60} \), leaving your answer in surd form.

Assessment: JAMB UTME - Mathematics - 2019 Subject: General Mathematics

Question 1 Report

\frac{2 \sqrt{3}}{3} + 10

\frac{3 \sqrt{2} - 1}{5}

\frac{3 \sqrt{2} + 1}{5}

\frac{2 \sqrt{3}}{3} - 10

Answer Details

\frac{2 \sin 30 + 5 \tan 60}{\sin 60}

\sin 30 = \frac{1}{2}; \tan 60 = \sqrt{3}; \sin 60 = \frac{\sqrt{3}}{2}

∴ \frac{2 \sin 30 + 5 \tan 60}{\sin 60} = \frac{2 (\frac{1}{2}) + 5 (\sqrt{3})}{\frac{\sqrt{3}}{2}}

\frac{1 + 5 \sqrt{3}}{\frac{\sqrt{3}}{2}}

\frac{2 (1 + 5 \sqrt{3})}{\sqrt{3}}

\frac{2 + 10 \sqrt{3}}{\sqrt{3}}

Rationalizing, we get
=

\frac{2 \sqrt{3} + 30}{3}

\frac{2}{3} \sqrt{3} + 10

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